When you say how much, do you mean measured by weight or measured by volume? If you measure by weight, the answer is the weight of water and ice remains the same. If you measure by volume then ice has a smaller density than water since it floats. When it melts it will be more dense and hence occupy less space. The combined volume will be less once the ice has melted. However, since the ice displaces a volume of water equal to its weight when it floats, then as it melts, the water level in the cup will remain constant as it melts.

Read carefully. The question asks for AMOUNT of water. Nothing has been said about the water LEVEL in the glass.
Let's say you have 2 cups of water.
The amount of water is 2 cups. Now freeze one cup and put it in a glass. Pour the unfrozen cup of water into the glass. Disregard any evaporization during the process. When the ice melts you still have 2 cups of water regardles of what the water level is.